I am admitted to both the PhD program at Columbia in Operations Research and the MASt Mathematical Statistics Part III at Cambridge and I don't really know what to choose.

My career goal is to work as a research machine learning scientist in a tech company (Google, Facebook, Amazon..etc).

Cheers

Focus on the project and what skills and experience you will gain. How are the labs organised and will you have a chance to publish. Do the labs have any links with the industry you are interested in and can you form networks with these companies and maybe spend some time in them?